Return to Revisions

One possible reason is that in higher dimensions there are more degrees of freedom that can be used to unravel and untangle things, which often leads to simpler structures. This reason has particularly been used as an explanation as to why the geometry/topology of high-dimensional manifolds is sometimes easier to deal with than that of lower dimensional ones. The canonical illustration that accompanies the previous sentence is the failure of the Whitney trick in dim < 5; the fact that the trick holds in higher dimensions was, for example, instrumental in Smale's proof of the $h$-cobordism theorem.